2.3.189 Problems 18801 to 18900

Table 2.961: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

18801

2481

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \end {array} \]

5.793

18802

12317

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +\frac {5 y}{4}&=0 \end {array} \]

5.793

18803

7746

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x -6 y&=0 \end {array} \]

5.797

18804

16993

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y&=0 \end {array} \]

5.798

18805

7534

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \end {array} \]

5.799

18806

777

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 y^{\prime } x +4 y&=0 \end {array} \]

5.803

18807

4874

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \end {array} \]

5.803

18808

19911

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=0\\ y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=1\\ \end {array} \]

5.803

18809

17173

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x +17 y&=0\\ y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=-3\\ \end {array} \]

5.804

18810

11821

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0\\ y \left (-1\right )&=2\\ y^{\prime }\left (-1\right )&=3\\ \end {array} \]

5.805

18811

19859

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=0\\ y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=-1\\ \end {array} \]

5.805

18812

27515

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]

5.805

18813

7509

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{4}+2 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]

5.809

18814

8274

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} m y^{\prime \prime }+k y&=0\\ y \left (0\right )&=a\\ y^{\prime }\left (0\right )&=b\\ \end {array} \]

5.809

18815

19809

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }-3 y&=3 \,{\mathrm e}^{2 t} \end {array} \]

5.811

18816

7683

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=3 \sin \left (2 t \right ) \end {array} \]

5.813

18817

16385

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }-3 y&=-3 t \,{\mathrm e}^{-t} \end {array} \]

5.814

18818

23912

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }&=3+4 \sin \left (2 t \right ) \end {array} \]

5.814

18819

3015

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=t^{2} {\mathrm e}^{3 t}+6 \end {array} \]

5.815

18820

4885

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=2 \,{\mathrm e}^{-t} \end {array} \]

5.816

18821

6968

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+4 y&=2 \,{\mathrm e}^{t} \end {array} \]

5.816

18822

8563

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=2 \,{\mathrm e}^{-t} \end {array} \]

5.820

18823

4139

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=3 \,{\mathrm e}^{-t} \end {array} \]

5.821

18824

11426

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }-4 y^{\prime }+y&=16 \,{\mathrm e}^{\frac {t}{2}} \end {array} \]

5.823

18825

14885

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+3 y^{\prime }+y&=t^{2}+3 \sin \left (t \right ) \end {array} \]

5.823

18826

21419

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=3 \sin \left (2 t \right )+t \cos \left (2 t \right ) \end {array} \]

5.824

18827

9886

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+w_{0}^{2} u&=\cos \left (w t \right ) \end {array} \]

5.830

18828

12291

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+4 y&=2 \sinh \left (t \right ) \end {array} \]

5.831

18829

22505

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=\cosh \left (2 t \right ) \end {array} \]

5.831

18830

27934

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&=2 t\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]

5.831

18831

7156

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=t^{2}+3 \,{\mathrm e}^{t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]

5.832

18832

4278

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} t +4\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]

5.833

18833

23154

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }-3 y&=3 \,{\mathrm e}^{2 t} t\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

5.835

18834

17077

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=3 \sin \left (2 t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]

5.837

18835

18655

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=4 \,{\mathrm e}^{-t} \cos \left (2 t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

5.837

18836

2097

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }&=2 t^{4}+t^{2} {\mathrm e}^{-3 t}+\sin \left (3 t \right ) \end {array} \]

5.838

18837

14833

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=t \left (1+\sin \left (t \right )\right ) \end {array} \]

5.839

18838

24813

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{t} \cos \left (2 t \right )+{\mathrm e}^{2 t} \left (3 t +4\right ) \sin \left (t \right ) \end {array} \]

5.839

18839

25472

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=3 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{-t} t^{2} \sin \left (t \right ) \end {array} \]

5.840

18840

2356

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=2 t^{2}+4 \,{\mathrm e}^{2 t} t +t \sin \left (2 t \right ) \end {array} \]

5.842

18841

12005

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=t^{2} \sin \left (2 t \right )+\left (6 t +7\right ) \cos \left (2 t \right ) \end {array} \]

5.842

18842

24814

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{t} \left (t^{2}+1\right ) \sin \left (2 t \right )+3 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{t} \end {array} \]

5.843

18843

5079

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }-4 y&=2 \,{\mathrm e}^{-t} \end {array} \]

5.845

18844

25179

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\ln \left (x \right ) \end {array} \]

5.846

18845

12480

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x \end {array} \]

5.847

18846

17240

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 x^{2}+2 \ln \left (x \right ) \end {array} \]

5.847

18847

22361

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=\sin \left (\ln \left (x \right )\right ) \end {array} \]

5.847

18848

800

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t \le \pi \\ \pi \,{\mathrm e}^{\pi -t} & \pi <t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]

5.849

18849

998

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0\le t \le \frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

5.849

18850

18691

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} A t & 0\le t \le \pi \\ A \left (2 \pi -t \right ) & \pi <t \le 2 \pi \\ 0 & 2 \pi <t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

5.849

18851

2844

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{4}+2 y&=2 \cos \left (w t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]

5.850

18852

19396

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=2 \cos \left (w t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

5.851

18853

18667

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=3 \cos \left (w t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]

5.852

18854

22564

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (\frac {t}{4}\right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

5.854

18855

25287

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (2 t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

5.854

18856

25657

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (6 t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

5.854

18857

27999

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y+\frac {y^{3}}{5}&=\cos \left (w t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

5.854

18858

11434

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5}&=\cos \left (w t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

5.855

18859

12496

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{t} \end {array} \]

5.857

18860

16139

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=2 \,{\mathrm e}^{-t} \end {array} \]

5.857

18861

16096

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=3 \,{\mathrm e}^{-t} \end {array} \]

5.860

18862

18591

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }-4 y^{\prime }+y&=16 \,{\mathrm e}^{\frac {t}{2}} \end {array} \]

5.863

18863

7023

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\tan \left (t \right ) \end {array} \]

5.866

18864

21825

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=3 \sec \left (2 t \right )^{2} \end {array} \]

5.867

18865

4822

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 t}}{t^{2}} \end {array} \]

5.868

18866

27488

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=2 \csc \left (\frac {t}{2}\right ) \end {array} \]

5.871

18867

18780

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+y&=2 \sec \left (2 t \right ) \end {array} \]

5.873

18868

19199

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{t}}{t^{2}+1} \end {array} \]

5.874

18869

12321

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+6 y&=g \left (t \right ) \end {array} \]

5.875

18870

12876

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=g \left (t \right ) \end {array} \]

5.876

18871

27462

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=2 t^{3} \end {array} \]

5.877

18872

25682

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y&={\mathrm e}^{2 t} t^{2} \end {array} \]

5.880

18873

14922

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-t \right ) y^{\prime \prime }+y^{\prime } t -y&=2 \left (t -1\right )^{2} {\mathrm e}^{-t} \end {array} \]

5.882

18874

26210

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=3 x^{{3}/{2}} \sin \left (x \right ) \end {array} \]

5.884

18875

5480

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=g \left (x \right ) \end {array} \]

5.885

18876

26880

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=g \left (x \right ) \end {array} \]

5.889

18877

6840

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-2 y&=3 t^{2}-1 \end {array} \]

5.892

18878

22553

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{2} \ln \left (x \right ) \end {array} \]

5.893

18879

12312

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=4 t^{2} \end {array} \]

5.898

18880

21355

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+7 y^{\prime } t +5 y&=t \end {array} \]

5.898

18881

27204

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=g \left (t \right )\\ y \left (0\right )&=y_{0}\\ y^{\prime }\left (0\right )&=y_{1}\\ \end {array} \]

5.898

18882

14692

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-\left (1+t \right ) y^{\prime }+y&={\mathrm e}^{2 t} t^{2} \end {array} \]

5.900

18883

24244

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-t \right ) y^{\prime \prime }+y^{\prime } t -y&=2 \left (t -1\right )^{2} {\mathrm e}^{-t} \end {array} \]

5.902

18884

26092

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-2 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]

Using Laplace transform method.

5.908

18885

1127

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 y^{\prime \prime }+12 y^{\prime }+4 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]

Using Laplace transform method.

5.912

18886

2311

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]

Using Laplace transform method.

5.914

18887

2483

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 y^{\prime \prime }+5 y^{\prime }+y&=0\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

5.914

18888

20499

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+2 y&=t^{2} {\mathrm e}^{t}+7\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]

Using Laplace transform method.

5.914

18889

4313

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }-6 y&=t^{2}+7\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

5.921

18890

18105

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=3 \,{\mathrm e}^{-2 t} \sin \left (2 t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]

Using Laplace transform method.

5.921

18891

24943

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=t \cos \left (2 t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

5.923

18892

18578

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=0\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=-2\\ \end {array} \]

Using Laplace transform method.

5.925

18893

10319

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-6 y&=t \,{\mathrm e}^{-t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=9\\ \end {array} \]

Using Laplace transform method.

5.928

18894

19907

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .\\ y \left (0\right )&=9\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]

Using Laplace transform method.

5.928

18895

25519

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

5.931

18896

12319

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

5.935

18897

22364

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }-12 y&=0\\ y \left (0\right )&=8\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

5.937

18898

8471

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=t\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

5.940

18899

10125

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-8 y^{\prime }+25 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]

Using Laplace transform method.

5.943

18900

25848

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]

Using Laplace transform method.

5.944